On the elastostatic analysis of mechanical systems

Taghvaeipour, Afshin; Ángeles, Jorge; Lessard, Larry

doi:10.1016/j.mechmachtheory.2012.07.011

Cited by 39 publications

(22 citation statements)

References 10 publications

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“…-Principal axis decomposition through congruence transformation by making use of the eigenvectors of the translational entry in the stiffness matrix -Decomposition of the dynamic inertia matrix by transforming variables into dimensionless parameters (Kövecses and Ebrahimi, 2009), which can be applied to the stiffness matrix (Taghvaeipour et al, 2012;Wu, 2014) -Decoupling of the stiffness matrix into translational and rotational parts (Angeles, 2010;Wu and Zou, 2016) It can be seen that the consistency problem in the stiffness measures have been remedied by not only homogenizing the Jacobian matrix as the source of the consistency problem, but also by decomposition and decoupling techniques applied directly to the stiffness matrix.…”

Section: Consistency Of Stiffness Measuresmentioning

confidence: 99%

Review article: Performance measures of parallel kinematics manipulators

2020

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Abstract. This extensive review paper, which involves 204 papers, discusses comprehensively a number of performance indices that are instrumental in the design of parallel kinematics manipulators. These indices measure the workspace as well as its quality including the distance to singularity, dexterity, manipulability, force transmission, accuracy, stiffness, and dynamic performance. After being classified, the indices are discussed in terms of some important aspects including definition, physical meaning soundness, dependency, consistency, scope of applicability, and computation cost. For the sake of completeness, some key mathematical expressions of the indices are provided.

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Section: Consistency Of Stiffness Measuresmentioning

confidence: 99%

Review article: Performance measures of parallel kinematics manipulators

2020

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“…• Decomposition of the dynamic inertia matrix by transforming variables into dimensionless parameters, which can be applied to the stiffness matrix [62,63].…”

Section: Stiffnessmentioning

confidence: 99%

Kinematic Performance Measures and Optimization of Parallel Kinematics Manipulators: A Brief Review

Rosyid¹,

El‐Khasawneh²,

Alazzam³

2017

Kinematics

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This chapter covers a number of kinematic performance indices that are instrumental in designing parallel kinematics manipulators. These indices can be used selectively based on manipulator requirements and functionality. This would provide the very practical tool for designers to approach their needs in a very comprehensive fashion. Nevertheless, most applications require a more composite set of requirements that makes optimizing performance more challenging. The later part of this chapter will discuss single-objective and multi-objectives optimization that could handle certain performance indices or a combination of them. A brief description of most common techniques in the literature will be provided.

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“…Calculation of the stiffness matrix Taghvaeipour et al 17 studied extensively the concept of generalized equivalent spring; as a case study, the 6 Â 6 Cartesian stiffness matrix of the McGill SMG was determined. In elastostatics, the mapping between the SAD screw of the MP and the wrench producing the SAD plays a central role.…”

Section: Generalized Coordinates and Generalized Velocitiesmentioning

confidence: 99%

“…17 In the elastodynamic analysis the potential energy of the robot is calculated in terms of the set of all independent generalized coordinates; hence, the potential energy of the McGill SMG, according to its elastodynamic model shown in Figure 2, the potential energy is obtained as…”

Section: Generalized Coordinates and Generalized Velocitiesmentioning

confidence: 99%

Elastodynamics of a two-limb Schönflies motion generator

Taghvaeipour

Ángeles

Lessard

2014

Proceedings of the Institution of Mechanical Engineers, Part C:

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The elastodynamic analysis of a two-limb Schönflies motion generators is the subject of this paper. This analysis calls for the calculation of the stiffness and mass matrices. By resorting to the generalized spring concept, the posture-dependent stiffness matrix of the robot is computed. With the motors locked, the motion caused by the flexible components leads to the robot mass matrix. The generalized springs help to simplify the model. Although this simplification filters out the higher natural frequencies, it eases the computation of the posture-dependent stiffness and mass matrices. This provides a valuable tool to simplify the evaluation of the robot performance from an elastodynamic point of view, while the robot executes a given task. Finally, the modal analysis of the McGill Schönflies motion generator, while executing a pickand-place operation, is conducted; under these conditions, the evolution of the first six natural frequencies is obtained. The elastodynamic performance of the robot for the given task is assessed using the results of the analysis.

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On the elastostatic analysis of mechanical systems

Cited by 39 publications

References 10 publications

Review article: Performance measures of parallel kinematics manipulators

Review article: Performance measures of parallel kinematics manipulators

Kinematic Performance Measures and Optimization of Parallel Kinematics Manipulators: A Brief Review

Elastodynamics of a two-limb Schönflies motion generator

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